The Demonstration Of Indispensability Of Quantum Computing In Quantum Simulation From A Perspective Of Representation

In recent yeas,researchers have not achieved satisfactory results in solving quantum multi-body problems.By studying the theory of representation,we found that the lack of suitable representation is the main reason for this failure.The purpose of this paper is to find the simplest form of wave function and the fastest and the most precise calculation method by studying the representation theory.With proper representation,we can reduce the difficulty of solving quantum multi-body problems and bring the possibility to accurately simulate quantum multi-body systems.In this paper,we summarized the previous work in the beginning,such as Fourier lattice points,orthogonal polynomial representations,wavelet representations,and window function representations.We found the application range and summarized the merits and shortcomings of these representations,as a consequence,we can put forward ideas for building new representations on the base of these representations.In this paper,we constructed a new representation:circularly discretized coherent state representation.This representation overcomes some shortcomings of the previous representations,and has high accuracy and high speed when dealing with quantum optics problems and harmonic oscillator problems.However,the circular discretized coherent state representation can only be used to deal with quantum optics problems and harmonic oscillator problems.For many-body problems,this representation does not perform well.At the end of the paper,we summarized the shortcomings of various representations running on classical computers,and concluded that there is no representation on classical computers which can accurately and quickly solve quantum multi-body problems.We made an outlook in the last part of the paper,demonstrating that it is possible for us to of solve quantum multi-body problems by combining quantum computers and Fock representation,which highlights the indispensability of quantum computing in quantum simulation.